Impuls-based dynamic simulation of higher order and numerical results

First, we will provide a short introduction to the impulse-based
method for dynamic simulation. Till now, impulses were
frequently used to resolve collisions between rigid bodies. In
the last years, we have extended these techniques to simulate
constraint forces. Important properties of the new impulse
method are: (1) Simulation in Cartesian coordinates, (2)
complete elimination of the constraint drift known from Lagrange
multiplier methods, (3) simple integration of collision and
friction and (4) real-time performance even for complex
multibody systems like six-legged walking machines. In order to
demonstrate the potential of the impulse-based method, we report
on numerical experiments. We compare the following dynamic
simulation methods: (1) Generalized (or reduced) coordinates,
(2) the Lagrange multiplier method with and without several
stabilization methods like Baumgarte, the velocity correction
and a projection method, (3) impulse-based methods of
integration order 2, 4, 6, 8, and 10. We have simulated the
mathematical pendulum, the double and the triple pendulum with
all of these dynamic simulation methods and report on the
attainable accuracy. ... mehrIt turned out that the impulse methods of
higher integration order are all of O(h3) but have very small
factors and are therefore relatively accurate. A Lagrange
multiplier method fully stabilized by impulse-based techniques
turned out to be the best of the Lagrange multiplier methods tested.